We study a multigrid method for non-Abelian lattice gauge theory, the time slice blocking, in two and four dimensions. For SU(2) gauge fields in two dimensions, critical slowing down is almost completely eliminated by this method. This result is in accordance with theoretical arguments based on the analysis of the scale dependence of acceptance rates for nonlocal Metropolis updates. The generalization of the time slice blocking to SU(2) in four dimensions is investigated analytically and by numerical simulations. Compared to two dimensions, the local disorder in the four-dimensional gauge field leads to kinematical problems.

On a two-dimensional lattice, the SU(2) gauge theory coupled to an unflavored fermion is formulated suitably for a Hamiltonian Monte Carlo calculation. This involves propagation through gauge-invariant states defined so that all transitions have positive amplitudes. The vacuum energy and the mass of the lightest baryon are discussed.